Evaluating Convergence Rates in Particle Swarm Optimization: Insights from Gradient-Perturbation and Dual-Binary Approaches

This paper investigates the convergence properties of two Particle Swarm Optimization (PSO) algorithms: the Gradient-Perturbation PSO and the Dual-Binary PSO. We introduce a novel evaluation criterion that quantifies the rate of convergence using a stochastic dynamic averaging approach, enabling a more precise analysis of the algorithms’ performance over time. Our theoretical contributions include explicit convergence bounds under mild assumptions, supported by rigorous probabilistic analysis. Through extensive experiments on benchmark optimization functions, we demonstrate that the proposed algorithms achieve competitive convergence speeds compared to standard PSO variants. These findings highlight the practical value and theoretical robustness of the new criterion in evaluating and enhancing PSO-based methods.